Answer:
Volume of water required to fill the pyramid is [tex]\frac{1}{3}[/tex]rd of the water required to fill the prism completely.
Step-by-step explanation:
Let Mr Jackson has an empty rectangular pyramid and rectangular prism.
Height and base of both are congruent.
So volume of rectangular pyramid [tex]V_{1}=\frac{1}{3}(\text{Area of the base})(\text{Height})[/tex]
[tex]V_{1}=\frac{1}{3}(A_{1})(h)[/tex]
Volume of the rectangular prism = (Area of the base)(height)
[tex]V_{2}=(A_{2})(h)[/tex]
[tex]\frac{V_{1}}{V_{2}}=\frac{\frac{1}{3}(A)h}{(A)h}[/tex] [ Since [tex]A_{1}= A_{2}[/tex] ]
[tex]\frac{V_{1}}{V_{2}}=\frac{1}{3}[/tex]
[tex]V_{1}=\frac{1}{3}(V_{2})[/tex]
Therefore, amount of water required to fill the pyramid is [tex]\frac{1}{3}[/tex]rd of the water required to fill the prism completely.
